{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 04\n",
    "\n",
    "# 二项式系数\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "526dd2a2-f689-4cb8-b155-8853d94eacfb",
   "metadata": {},
   "source": [
    "该代码通过计算二项式$(x + 1)^n$的展开式，提取各项系数并绘制其分布图，以展示不同幂次下二项式系数的变化情况。具体来说，对于不同的$n$值（如$4, 8, 12, 5, 9, 13, 36$），代码依次展开$(x + 1)^n$，将其表示为多项式形式：\n",
    "\n",
    "$$\n",
    "(x + 1)^n = \\sum_{k=0}^{n} \\binom{n}{k} x^k\n",
    "$$\n",
    "\n",
    "其中，$\\binom{n}{k}$表示第$k$项的系数。代码提取每个展开式的系数列表$\\{\\binom{n}{0}, \\binom{n}{1}, \\dots, \\binom{n}{n}\\}$，并在图形中绘制这些系数随阶次（从$0$到$n$）的分布。\n",
    "\n",
    "### 主要步骤\n",
    "\n",
    "1. **多项式展开**：计算$(x + 1)^n$的展开式，并提取各项系数，得到一个包含二项式系数的列表。\n",
    "   \n",
    "2. **绘制系数分布图**：使用`stem`图展示各项的系数值，横轴为多项式的阶次，纵轴为对应的系数值。设置横轴从$n$至$0$的递减顺序，使最高次项显示在左侧。\n",
    "\n",
    "### 数学意义\n",
    "\n",
    "二项式定理表明，$(x + 1)^n$的展开式中的系数遵循二项式分布，随着$n$的增加，这些系数逐渐形成对称的分布，接近正态分布。这一现象在概率论中称为二项分布的正态逼近：\n",
    "\n",
    "$$\n",
    "\\binom{n}{k} \\approx \\frac{1}{\\sqrt{2 \\pi n p (1-p)}} e^{-\\frac{(k - np)^2}{2np(1-p)}}\n",
    "$$\n",
    "\n",
    "其中$p = 0.5$。该代码通过可视化不同$n$下的系数分布，展示了二项式展开的对称性和逼近性。随着$n$增大，系数分布趋向于正态分布，这是二项分布向正态分布收敛的直观体现。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fdb62a2b-a38f-4e2a-8358-e1dc6849681d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 4, 6, 4, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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HjoiI0HfffSdJevjhh3X27NlaGcjtdpc7jgUAAOCSKofLhQsXvAfDvv322yotLa3xg2dkZGjTpk06cuSIdu7cqYyMDG3YsEEpKSk13jYAALj2VPmtoqSkJCUnJ6tnz57yeDyaNGmSGjRoUOm6b731VpW2WVhYqNGjR+vEiRNyOBzq1q2bVq9eXa2T2AEAgOtHlcPl3Xff1V/+8hcdPHhQkuR0Omu81+Vvf/tbje4PAACuL1UOl6ioKM2cOVOSFBsbqwULFqhZs2a1NhgAAMD/8ung3P79+yskJKTWhgIAAKiMpQfnAgAAVIelB+cCAABUh08H59psNr8cnAsAAFAdHJwLAACM4dO3Qx8+fNj769LSUoWGhvptIAAAgCup8sG5l3O73XruuefUqlUrNW7cWIcOHZIkPf3005ybBQAA1BqfwuX555/X/Pnz9eKLL5b7WHSXLl305ptv+m04AACAy/kULu+8847eeOMNpaSkKCgoyLs8Pj5ee/fu9dtwAAAAl/MpXI4fP6727dtXWO52u3Xx4sUaDwUAAFAZn8IlLi5OmzdvrrB86dKl6tGjR42HAgAAqIxPnyqaNm2aUlNTdfz4cbndbi1btkz79u3TO++8o5UrV/p7RgAAAEk+7nEZNWqUPvzwQ61du1aNGjXStGnTtGfPHn344YcaPHiwv2cEAACQ5OMeF0m67bbbtGbNGn/OAgAAcFU+h4sk5eXlac+ePZKkzp07c3wLAACoVT6FS2Fhoe6//35t2LBBTZo0kSSdOXNG/fv31+LFi9W8eXN/zggAACDJx2NcJk6cqLNnz+qrr77S6dOndfr0ae3atUtFRUWaNGmSv2cEAACQ5OMel5ycHK1du1adOnXyLouLi9OcOXM0ZMgQvw0HAABwOZ+/q6h+/foVltevX19ut7vGQwEAAFTGp3AZMGCAJk+erG+//da77Pjx43r88cc1cOBAvw0HAABwOZ/CZfbs2SoqKlK7du1000036aabblJsbKyKior06quv+ntGAAAAST4e4xITE6Pt27dr7dq13i9V7NSpkwYNGuTX4QAAAC5XrT0u69evV1xcnIqKimSz2TR48GBNnDhREydOVK9evdS5c+dKv8MIAADAH6oVLrNmzdL48eMVHh5e4TaHw6Ff//rXevnll/02HAAAwOWqFS47duzQsGHDrnj7kCFDlJeXV+OhAAAAKlOtcDl58mSlH4O+JDg4WKdOnarxUAAAAJWpVri0atVKu3btuuLtX375paKjo2s8FAAAQGWqFS533HGHnn76aZWWlla47fz585o+fbpGjBjht+EAAAAuV62PQz/11FNatmyZOnTooAkTJqhjx46SpL1792rOnDkqKyvTk08+WSuDAgAAVCtcoqKi9Omnn+qxxx5TRkaGPB6PJMlms2no0KGaM2eOoqKiamVQAACAap+Arm3btvr444/1/fff68CBA/J4PLr55pvVtGnT2pgPAADAy6cz50pS06ZN1atXL3/OAgAAcFU+fVcRAACAFQgXAABgDMIFAAAYg3ABAADGIFwAAIAxCBcAAGAMwgUAABiDcAEAAMYgXAAAgDEIFwAAYAzCBQAAGINwAQAAxiBcAACAMQgXAABgDMIFAAAYg3ABAADGIFwAAIAxLA2XrKws9erVS2FhYYqMjFRycrL27dtn5UgAACCAWRouGzduVFpamrZs2aI1a9bo4sWLGjJkiEpKSqwcCwAABKhgKx88Jyen3PX58+crMjJSeXl56tevn0VTAQCAQBVQx7g4nU5JUkREhMWTAACAQGTpHpfLud1uTZkyRX379lWXLl0qXcflcsnlcnmvFxUV1dV4AAAgAATMHpe0tDTt2rVLixcvvuI6WVlZcjgc3ktMTEwdTggAAKwWEOEyYcIErVy5Uv/617/UunXrK66XkZEhp9PpvRw7dqwOpwQAAFaz9K0ij8ejiRMnavny5dqwYYNiY2Ovur7dbpfdbq+j6QAAQKCxNFzS0tK0aNEirVixQmFhYSooKJAkORwONWjQwMrRAABAALL0raLs7Gw5nU7dfvvtio6O9l6WLFli5VgAACBAWf5WEQAAQFUFxMG5AAAAVUG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAY1wT4bL10GmVuT1WjwEAAH5Cmdujzw7+Vyvyj/t0f0vDZdOmTRo5cqRatmwpm82m999/36ftPPx2rn72p/XK2XXCvwMCAAC/ydl1Qj/703o9MG+LJi/O92kbloZLSUmJ4uPjNWfOnBpvq8BZqsfe3U68AAAQgHJ2ndBj727XCWdpjbYT7Kd5fDJ8+HANHz7cL9vySLJJyvxwtwbHtVBQPZtftgsAAGqmzO1R5oe75Y+DOow6xsXlcqmoqKjc5XIeSSecpdp6+LQ1AwIAgAq2Hj5d4z0tlxgVLllZWXI4HN5LTExMpesVnvXPHw4AAKg5f/67bFS4ZGRkyOl0ei/Hjh2rdL3IsNA6ngwAAFyJP/9dtvQYl+qy2+2y2+1XvN0mqYUjVL1jI+puKAAAcFW9YyMU7QhVgbO0xse5GLXH5WouHYo7fWQcB+YCABBAgurZNH1knKT/+/faV5aGS3FxsfLz85Wfny9JOnz4sPLz83X06NFqb6uFI1TZDyVoWJdoP08JAABqaliXaGU/lKDI8Cu/c1IVlr5VtG3bNvXv3997PT09XZKUmpqq+fPnV3k72Q8laFiPG9nTAgBAABvWJVp929+grs/8U6/c392nbVgaLrfffrs8npp/qrtn26ZECwAABrj07/Wo7q18uv81c4wLAAC49hEuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABjEC4AAMAYhAsAADAG4QIAAIxBuAAAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwRkCEy5w5c9SuXTuFhoaqT58+2rp1q9UjAQCAAGR5uCxZskTp6emaPn26tm/frvj4eA0dOlSFhYVWjwYAAAJMsNUDvPzyyxo/frzGjh0rSXr99df10Ucf6a233tLUqVOrtA33uXNynwutzTFhMfeFH2T/wfXjr8+dk/sHy//qohbxfF9feL6vL5c/376weTwejx/nqZYLFy6oYcOGWrp0qZKTk73LU1NTdebMGa1YsaLc+i6XSy7X//1mnU6n2rRpo/U33qjG9YLqamwAAFBDHfO2KSwsTDabrVr3szRrv/vuO5WVlSkqKqrc8qioKO3du7fC+llZWcrMzKywfMChQ7U2IwAAqAUOhwoLC9W8efNq3c2o/XEZGRlKT0/3Xj9z5ozatm2ro0ePyuFwWDgZ6kJRUZFiYmJ07NgxhYeHWz0OahnP9/WF5/v6cun5DgkJqfZ9LQ2XG264QUFBQTp58mS55SdPnlSLFi0qrG+322W32yssdzgc/EW/joSHh/N8X0d4vq8vPN/Xl+q+TSRZ/KmikJAQ9ezZU+vWrfMuc7vdWrdunZKSkiycDAAABCLL3ypKT09XamqqEhMT1bt3b82aNUslJSXeTxkBAABcYnm43HfffTp16pSmTZumgoICde/eXTk5ORUO2K2M3W7X9OnTK337CNcenu/rC8/39YXn+/pSk+fb0o9DAwAAVIflZ84FAACoKsIFAAAYg3ABAADGIFwAAIAxjA+XmTNnymazacqUKVaPglqSnZ2tbt26eU9MlZSUpFWrVlk9FmpJVlaWevXqpbCwMEVGRio5OVn79u2zeizUkk2bNmnkyJFq2bKlbDab3n//fatHQh2YM2eO2rVrp9DQUPXp00dbt26t8n2NDpfc3FzNnTtX3bp1s3oU1KLWrVtr5syZysvL07Zt2zRgwACNGjVKX331ldWjoRZs3LhRaWlp2rJli9asWaOLFy9qyJAhKikpsXo01IKSkhLFx8drzpw5Vo+COrJkyRKlp6dr+vTp2r59u+Lj4zV06FAVFhZW6f7Gfhy6uLhYCQkJeu211/T888+re/fumjVrltVjoY5ERETopZde0iOPPGL1KKhlp06dUmRkpDZu3Kh+/fpZPQ5qkc1m0/Lly5WcnGz1KKhFffr0Ua9evTR79mxJP54xPyYmRhMnTtTUqVN/8v7G7nFJS0vTnXfeqUGDBlk9CupQWVmZFi9erJKSEr4W4jrhdDol/RirAMx24cIF5eXllfu3u169eho0aJA+++yzKm3D8jPn+mLx4sXavn27cnNzrR4FdWTnzp1KSkpSaWmpGjdurOXLlysuLs7qsVDL3G63pkyZor59+6pLly5WjwOghr777juVlZVVODt+VFSU9u7dW6VtGBcux44d0+TJk7VmzRqFhoZaPQ7qSMeOHZWfny+n06mlS5cqNTVVGzduJF6ucWlpadq1a5f+/e9/Wz0KgABhXLjk5eWpsLBQCQkJ3mVlZWXatGmTZs+eLZfLpaCgIAsnRG0ICQlR+/btJUk9e/ZUbm6uXnnlFc2dO9fiyVBbJkyYoJUrV2rTpk1q3bq11eMA8IMbbrhBQUFBOnnyZLnlJ0+eVIsWLaq0DeOOcRk4cKB27typ/Px87yUxMVEpKSnKz88nWq4TbrdbLpfL6jFQCzwejyZMmKDly5dr/fr1io2NtXokAH4SEhKinj17at26dd5lbrdb69atq/Jxi8btcQkLC6vwXnejRo3UrFkz3gO/RmVkZGj48OFq06aNzp49q0WLFmnDhg1avXq11aOhFqSlpWnRokVasWKFwsLCVFBQIElyOBxq0KCBxdPB34qLi3XgwAHv9cOHDys/P18RERFq06aNhZOhtqSnpys1NVWJiYnq3bu3Zs2apZKSEo0dO7ZK9zcuXHD9KSws1OjRo3XixAk5HA5169ZNq1ev1uDBg60eDbUgOztbknT77beXW/73v/9dY8aMqfuBUKu2bdum/v37e6+np6dLklJTUzV//nyLpkJtuu+++3Tq1ClNmzZNBQUF6t69u3JyciocsHslxp7HBQAAXH+MO8YFAABcvwgXAABgDMIFAAAYg3ABAADGIFwAAIAxCBcAAGAMwgUAABiDcAEAAMYgXAD4bMyYMbLZbLLZbKpfv76ioqI0ePBgvfXWW3K73VaPB+AaRLgAqJFhw4bpxIkTOnLkiFatWqX+/ftr8uTJGjFihH744Ydae9wLFy7U2rYBBC7CBUCN2O12tWjRQq1atVJCQoL++Mc/asWKFVq1apX3u2bOnDmjcePGqXnz5goPD9eAAQO0Y8eOctt5/vnnFRkZqbCwMI0bN05Tp05V9+7dvbePGTNGycnJmjFjhlq2bKmOHTtKko4dO6Z7771XTZo0UUREhEaNGqUjR46U2/abb76pTp06KTQ0VLfccotee+212vwjAVCLCBcAfjdgwADFx8dr2bJlkqR77rlHhYWFWrVqlfLy8pSQkKCBAwfq9OnTkqSFCxdqxowZ+tOf/qS8vDy1adPG+2WLl1u3bp327dunNWvWaOXKlbp48aKGDh2qsLAwbd68WZ988okaN26sYcOGeffILFy4UNOmTdOMGTO0Z88evfDCC3r66af19ttv190fCAD/8QCAj1JTUz2jRo2q9Lb77rvP06lTJ8/mzZs94eHhntLS0nK333TTTZ65c+d6PB6Pp0+fPp60tLRyt/ft29cTHx9f7rGioqI8LpfLu2zBggWejh07etxut3eZy+XyNGjQwLN69Wrv4yxatKjctp977jlPUlJStX+/AKwXbHU4Abg2eTwe2Ww27dixQ8XFxWrWrFm528+fP6+DBw9Kkvbt26ff/OY35W7v3bu31q9fX25Z165dFRIS4r2+Y8cOHThwQGFhYeXWKy0t1cGDB1VSUqKDBw/qkUce0fjx4723//DDD3I4HH75fQKoW4QLgFqxZ88excbGqri4WNHR0dqwYUOFdZo0aVKtbTZq1Kjc9eLiYvXs2VMLFy6ssG7z5s1VXFwsSZo3b5769OlT7vagoKBqPTaAwEC4APC79evXa+fOnXr88cfVunVrFRQUKDg4WO3atat0/Y4dOyo3N1ejR4/2LsvNzf3Jx0lISNCSJUsUGRmp8PDwCrc7HA61bNlShw4dUkpKis+/HwCBg3ABUCMul0sFBQUqKyvTyZMnlZOTo6ysLI0YMUKjR49WvXr1lJSUpOTkZL344ovq0KGDvv32W3300Ue66667lJiYqIkTJ2r8+PFKTEzUrbfeqiVLlujLL7/UjTfeeNXHTklJ0UsvvaRRo0bp2WefVevWrfXNN99o2bJl+v3vf6/WrVsrMzNTkyZNksPh0LBhw+RyubRt2zZ9//33Sk9Pr6M/JQD+QrgAqJGcnBxFR0crODhYTZs2VXx8vP76178qNTVV9er9+MHFjz/+WE8++aTGjh2rU6dOqUWLFurXr5+ioqIk/Rgghw4d0hNPPKHS0lLde++9GjNmjLZu3XrVx27YsKE2bdqkP/zhD7r77rt19uxZtWrVSgMHDvTugRk3bpwaNmyol156Sb/73e/UqFEjde3aVVOmTKnVPxcAtcPm8Xg8Vg8BAP9r8ODBatGihRYsWGD1KAACCHtcAFju3Llzev311zV06FAFBQXpvffe09q1a7VmzRqrRwMQYNjjAsBy58+f18iRI/XFF1+otLRUHTt21FNPPaW7777b6tEABBjCBQAAGINT/gMAAGMQLgAAwBiECwAAMAbhAgAAjEG4AAAAYxAuAADAGIQLAAAwBuECAACMQbgAAABj/H/Hb7TufvMyCgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 8, 28, 56, 70, 56, 28, 8, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 5, 10, 10, 5, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 9, 36, 84, 126, 126, 84, 36, 9, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 36, 630, 7140, 58905, 376992, 1947792, 8347680, 30260340, 94143280, 254186856, 600805296, 1251677700, 2310789600, 3796297200, 5567902560, 7307872110, 8597496600, 9075135300, 8597496600, 7307872110, 5567902560, 3796297200, 2310789600, 1251677700, 600805296, 254186856, 94143280, 30260340, 8347680, 1947792, 376992, 58905, 7140, 630, 36, 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 展开多项式并绘制其系数图\n",
    "from sympy.abc import x, a\n",
    "from sympy import Poly\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "for n in [4, 8, 12, 5, 9, 13, 36]:  # 迭代不同次幂的多项式\n",
    "    \n",
    "    expr = (x + 1)**n  # 定义多项式表达式\n",
    "    expr_expand = expr.expand()  # 展开多项式\n",
    "    expr_expand = Poly(expr_expand)  # 转换为多项式形式\n",
    "    \n",
    "    poly_coeffs = expr_expand.coeffs()  # 获取多项式的系数列表\n",
    "    \n",
    "    print(poly_coeffs)  # 输出系数列表\n",
    "    \n",
    "    degrees = np.linspace(n, 0, n + 1)  # 定义多项式的阶次\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    plt.stem(degrees, np.array(poly_coeffs, dtype=float))  # 绘制系数的分布图\n",
    "    plt.xlim(0, n)  # 设置x轴范围\n",
    "    plt.xticks(np.arange(0, n+1))  # 设置x轴刻度\n",
    "    y_max = max(poly_coeffs)  # 获取系数的最大值\n",
    "    y_max = float(y_max)\n",
    "    plt.ylim(0, y_max)  # 设置y轴范围\n",
    "    \n",
    "    ax.spines['right'].set_visible(False)  # 隐藏右侧边框\n",
    "    ax.spines['top'].set_visible(False)  # 隐藏顶部边框\n",
    "    ax.invert_xaxis()  # 翻转x轴\n",
    "    plt.xlabel('Degree')  # 设置x轴标签\n",
    "    plt.ylabel('Coefficient')  # 设置y轴标签\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
